Large language models for vertical domains are bottlenecked by the scarcity of complex, domain-specific task-oriented dialogues. Existing data acquisition pipelines face a persistent trilemma: expert annotation is expensive, real-world service conversations are constrained by privacy and commercial restrictions, and static corpora quickly become temporally stale. We propose Stream, a data-centric framework that leverages publicly available streaming media (live streams and short videos) to synthesize high-value service dialogues at scale. Stream mines authentic interaction signals from noisy streams and synthesizes conversations by integrating role-grounded persona construction with Conversational Blueprint construction; it further adopts retrieval-augmented generation (RAG) to support knowledge-aware responses. Based on Stream, we release StreamDial, a large-scale multi-domain dataset covering Automotive, Restaurant, and Hotel. StreamDial contains 87,498 dialogue sessions and 1,497,320 turns in total, with an average of 17.11 turns per session and a comparable scale across domains. Each session is organized as a structured quadruplet $\langle P_u, P_a, B, H \rangle$ that pairs dialogue history with explicit user/agent personas and a Conversational Blueprint, capturing realistic service behaviors such as requirement mining, constraint conflicts, negotiation, and recovery. Evaluations with automatic judges and downstream tasks show that StreamDial improves intrinsic dialogue quality over strong baselines, and models trained with StreamDial improve Dialogue State Tracking across backbones; we further report a completed human-evaluation set and encouraging multilingual transfer on Qwen3-8B under a controlled training budget. The data is released in https://github.com/hitxueliang/DialogDataSetBySTREAM.